a simple doubt

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The orthogonal trajectory of x² + y² = a² , where'a' is arbitrary constant is a circle.
IS THE STATEMENT RIGHT???????

#Mathematics #Co-ordinate Geometry

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7 Answers

1

Arshad ~Died~ ·2009-11-02 03:14:31

...no statement is false

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UTTARA ·2009-11-02 03:16:47

Arshad post the Reason Plzz :)

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Arshad ~Died~ ·2009-11-02 03:43:55

just find the orthogonal trajectory-it will come out to be a line

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106

Asish Mahapatra ·2009-11-02 05:12:41

Think of concentric circles
They represent equipotential surfaces of a point charge placed at the centre (in 2D neglecting the 3rd dimension)

Now, orthogonal trajectory is perp. to all of these circles
Also electric field is perpendicular to potential surfaces.

Now electric field of a point charge is straight lines passing thru the charge

So orthogonal trajectory of concentric circles is the system of straight lines passing thru the centre (in this case origin)

So, the orthogonal trajectory is y=mx

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Arshad ~Died~ ·2009-11-02 07:09:41

dats an awesome explanation dude.....!!!

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Unicorn--- Extinct!! ·2009-11-02 10:13:14

[5]

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UTTARA ·2009-11-02 23:41:09

Thanks Asish & Arshad

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Your Answer

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